Definition of Convergence

Asked Dec 27 '19 at 03:24

Active Dec 27 '19 at 03:24

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What is the definition of convergence? The reason why I'm asking this question is to understand why $\frac1x$ diverges and $\frac1{x^2}$ converges.

The $\lim_{x\to\infty}\frac1x=0$ as does $\lim_{x\to\infty}\frac1{x^2}$. So why is one convergent and one divergent?

asked Dec 27 '19 at 03:24

Burt

3

are you asking about divergence vs. convergence of the series $\Sigma \dfrac1x$ and $\Sigma \dfrac1{x^2}$? – J. W. Tanner Dec 27 '19 at 03:29
@J.W.Tanner yes - especially seeing as they both have a finite limit. – Burt Dec 27 '19 at 03:31
Does this answer your question? Why does the harmonic series diverge but the p-harmonic series converge – MoonLightSyzygy Dec 27 '19 at 03:37
You seem to be confusing convergence/divergence of the sequence $(a_n){1}^{\infty}$ with convergence/divergence of the series $\sum{1}^{\infty} a_n$. – Hans Lundmark Dec 27 '19 at 09:34

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